a diverging lens forms an image 1/3 rd the size of an object that is 24 cm away from the lens. determine the focal length of the lens.

Diverging lens :

object height = h

image height = h/3

object distance (u) = - 24 cm

v = ?

f = ?

m = H/h =h/3/h = h/3h = 1/3

m = 1/3

m = -v/u

1/3 = -v/-24

v = 8 cm

Now by lens formulae,

1/f = 1/v -1/u

1/f = 1/8 - (-1/24)

1/f = 1/8 + 1/24

     = 3 + 1/24

     = 4/24

     = 1/6

   f = 6 cm

Hence the focal length of the lens will be 6 cm.

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